For example, for manufacturing semiconductor devices or the like, a material fluid, such as a suitable reactant gas, is supplied onto a substrate to form thereon a semiconductor layer, an insulating film, an electric conductive layer, or the like, or to etch or clean a surface thereof, or to form a coating member. Such a process, which has been widely employed also in fields other than semiconductor device manufacturing, can be referred to as surface treatment in a broad sense, and an apparatus for surface treatment can be referred to as a surface treatment apparatus in a broad sense.
For example, surface treatment apparatuses in a broad sense include an epitaxial apparatus for epitaxial growth of a semiconductor layer on a semiconductor wafer, an insulating wafer, or the like; a chemical vapor deposition (CVD) apparatus for depositing a thin film, such as a suitable oxide film or the like, on a semiconductor wafer; a dry-etching apparatus for removing a thin film or the like formed on a semiconductor wafer; and so forth.
The surface treatment apparatuses include a horizontal type in which a surface treatment material fluid is supplied in a direction in parallel to a surface of a substrate, and a vertical type in which a surface treatment material fluid is supplied in a direction substantially perpendicular to a surface of a substrate. In the latter, in order to ensure uniformity in surface treatment, the substrate is often rotated around an axis extending in the direction perpendicular to a surface of the substrate.
Such vertical-type rotary-surface treatment apparatuses are used for various uses, and have common features in the following points. That is, (1) a treatment target object having a treatment target surface of any of various shapes is placed in the middle of the apparatus and then rotated, (2) material gas or liquid is supplied from above the apparatus so that a boundary layer is formed near the surface of the treatment target object through rotation, (3) phase transition and chemical reaction is caused on the surface or in the boundary layer, whereby an effect of surface treatment is obtained, and (4) a fluid flows from the middle to an outside end portion of the treatment target object due to centrifugal force. As described above, in a vertical-type rotary surface treatment apparatus, a treatment target object is not necessarily a flat substrate, and a vertical-type rotary surface treatment apparatus can be used with a treatment target object of various shapes.
As described above, a feature of a vertical-type rotary surface treatment apparatus may include uniformity in distribution of physical parameters such as a boundary layer thickness, temperature, density, and so forth, in a boundary layer formed by rotating a treatment target object. Such uniform operation condition can lead to occurrence of uniform physical and chemical reactions on the surface, thus improving uniformity of products.
For example, Patent Document 1 describes that, in a CVD apparatus for forming an epitaxial growth layer on a surface of a semiconductor substrate, rotation of a wafer at a high speed such as a few hundreds of rotations per minute or faster causes a drop in the pressure near the wafer so that reactant gas supplied from above the wafer is drawn (pump effect) to the wafer surface, and, moreover, a boundary layer immediately above the wafer surface where epitaxial growth reaction is progressing is leveled to be thinner, to thereby improve efficiency in supplying reactant gas and thus the speed of epitaxial growth.
Regarding analysis on the pump effect, non-patent document 1 describes an example of an exact solution to the Navier-Stokes equation as to a flow around a disk rotating, in fluid around an axis perpendicular to a flat surface at a constant angular speed ω. In the document, it is described that the thickness of the boundary layer can be approximated to (ν/ω)1/2 in terms of as a kinematic viscosity coefficient ν of the fluid. And using normalization by a dimensionless distance z/(ν/ω))1/2 where z is a distance along the axial direction, a 4-dimensional simultaneous partial differential equation, in terms of the speed u in the radial direction of the disk, the circumferential directional speed ν, the axial directional speed w, and the pressure p, should be solved.
The calculation result shows that the axial directional speed w of the fluid due to the pump effect becomes smaller as the distance alone the axial direction becomes shorter while approaching the disk to become zero on a surface of the disk, and that the radial directional speed u shows a distribution in which the radial directional speed u is zero on a disk surface, then gradually increases with the distance along the axial direction, and returns to zero again as the distance becomes much longer.
Although the effect of temperature is not taken into consideration in non-patent document 1, non-patent document 2 describes that, as a technology for forming silicon on a rotating disk, solution of a 5-dimensional simultaneous partial differential equation with respect to a heat energy equation in consideration of heat conductivity of fluid, in addition to the 4-dimensional simultaneous partial differential equation described in non-patent document 1.